Is dhikr (the remembrance of Allah) an innovation?

The remembrance of Allah is not a reprehensible innovation: it is among the greatest of the supererogatory works of worship. Even self-composed supplications and the use of counting-beads have a basis in the Prophet's ﷺ own encouragement and his household.

Some question whether these supplications, and the counting beads, are a reprehensible innovation. The Sunnah itself answers this: the Prophet ﷺ encouraged supplications that were not part of the Sunnah.

As authenticated by the hadith, Burayda may Allah be pleased with him said, “I entered the Masjid with the Messenger ﷺ, where a man was supplicating; ‘O Allah, I ask you by the fact that I testify, You are Allah, there is no god but You, the One, the Ultimate, who did not beget and was not begotten, and to whom no one is equal,’ and the Prophet ﷺ said, ‘By Him in whose hands is my soul, he has asked Allah by His Greatest name, which if He is asked by it He gives, and if supplicated, He answers.’” [Sahih Ibn Hibban 892]

As for the counting beads, the following hadith is the basis for the counters: Saffiyah may Allah be pleased with her the Mother of the believers, narrated that the Messenger ﷺ came to her when she had in front of her four thousand date pits which she was using as counters for glorification of Allah. [Jami at-Tirmidhi 3554]

The scholars hold that a supplication in one's own time and one's own way does not become a reprehensible innovation unless it competes against a specific Sunnah legislated for that time and place. Otherwise, calling on Allah in one's own words is what the Prophet ﷺ himself encouraged, and keeping count of it is what his own household practiced.